Visualizing Returns
Kerry Back
BUSI 721, Fall 2022
JGSB, Rice University
Let’s look at the history of stock market returns – either the U.S. market as a whole or individual stocks or funds.
Four different plots
- scatter plot of returns by year
- box plot of annual returns
- accumulations \((1+r_1)(1+r_2) \cdots (1+r_n)\) by \(n\)
- accumulations with log scale
Box Plot
Box contains 25th percentile through 75th percentile
Median is indicated as a line in the box
Fences extend 1.5 times inter-quartile range from 25th and 75th percentiles or to the most extreme observation if that is closer to the box
- inter-quartile range = 75th minus 25th percentile)
Points outside the fences are outliers
- if you simulate data from a normal distribution, there will typically be very few points outside the fences
Why log plots? An Example
- Let’s look at accumulations from two hypothetical stocks.
- stock 1: 10% per year
- stock 1: 2% per year until 2000 and 10% afterwards
- It will appear that stock 2 did nothing before 2000 and earned a lot less than stock 1 even after 2000.
Log (base 10) of accumulation
Map \(y\) tick labels to dollars